San Diego  Nathan Fletcher’s quest to capture the mayor’s office from the political center continues to come under attack as opponents on Monday questioned his changing affiliations and which of his former supporters he would now disavow.

“How can voters trust you to stand up and not change your mind when it’s politically convenient?” GOP-backed candidate City Councilman Kevin Faulconer asked during a KPBS/10News debate.

The Democratic Party backed candidate, City Councilman David Alvarez, asked Fletcher about his past support from Republican stalwarts George W. Bush adviser Karl Rove, former Republican Gov. Pete Wilson and 2012 GOP presidential nominee Mitt Romney.

“Which one of those do you still admire, and why?” Alvarez asked.

Fletcher responded that he’s willing to work with anyone.

“Voters can trust that I am always going to do what is right for the city — they can trust I’m going to look out for them,” Fletcher said. “This is your typical partisan politics. I want to make a real clear statement — I’ll take the support of anyone out there.”

Fletcher’s history of switching his registration from Republican to independent last year to now Democrat has dogged him since he entered the Nov. 19 special election to replace Bob Filner. Throughout the noontime debate, the Qualcomm executive and former assemblyman sought to deflect the attacks by portraying himself as not beholden to anyone. His candidacy, he said, was about creating 130,000 jobs by 2020 and doing what’s right for all San Diegans.

“You won’t need a lobbyist to get in to see me at City Hall,” he said.

Faulconer emphasized his seven-year history as a councilman and work to help guide the city out of near financial ruin. He vowed to continue to guard city finances, streamline regulations and eliminate red tape so the world would know San Diego “is open for business.”

“I have the experience and leadership that’s ready to go on day one,” he said.

Alvarez stressed his advocacy for the city’s neighborhoods, said he would forbid a “pay to play” culture at City Hall and that he is “not about promises, I’m about action.”

“I am the only one who is endorsed by the Democratic Party, and that makes a difference. I want to make sure that we actually invest in our neighborhoods. We have not invested in the way that we need to in the city.”

Former City Attorney Mike Aguirre, whom polls show running a distant fourth, repeatedly talked about the need for more pension reform to free up city dollars for infrastructure needs.

Asked whether they would support public financing for a new San Diego Chargers stadium, Alvarez was opposed while Fletcher said he thinks there is a way to include taxpayer support outside of general fund dollars. Aguirre said voters should decide at the ballot box, while Faulconer said he would need to see the details first.

After the debate, the Fletcher camp defended his remark that he has the backing of Gov. Jerry Brown. The governor praised Fletcher while in San Diego last week but stopped short of an outright endorsement.

“He believes he has the support of the governor,” spokeswoman Janine Pairis, said of Fletcher’s comment.